Effect of coefficient of restitution in Euler-Euler CFD simulation of fluidized-bed hydrodynamics

Collision between particles plays an important role in determining the hydrodynamic characteristics of gas-solid flow in a fluidized bed. In the present work, earlier work （Loha, Chattopadhyay, ＆ Chatterjee, 2013） was extended to study the effect of the elasticity of particle collision on the hydrodynamic behavior of a bubbling fluidized bed filled with 530-~m particles. The Eulerian-Eulerian two-fluid model was used to simulate the hydrodynamics of the bubbling fluidized bed, where the solid-phase properties were calculated by applying the kinetic theory of granular flow. To investigate the effect of the elasticity of particle collision, different values of the coefficient of restitution were applied in the simulation and their effects were studied in detail. Simulations were performed for two different solid-phase wall boundary conditions. No bubble formation was observed for perfectly elastic collision. The bubble formation started as soon as the coefficient of restitution was set below 1.0, and the space occupied by bubbles in the bed increased with a decrease in the coefficient of restitution. Simulation results were also compared with experimental data available in the literature, and good agreement was found for coefficients of restitution of 0.95 and 0.99.

A stability condition for turbulence model:From EMMS model to EMMS-based turbulence model

The closure problem of turbulence is still a challenging issue in turbulence modeling. In this work, a stability condition is used to close turbulence. Specifically, we regard single-phase flow as a mixture of turbulent and non-turbulent fluids, separating the structure of turbulence. Subsequently, according to the picture of the turbulent eddy cascade, the energy contained in turbulent flow is decomposed into different parts and then quantified. A turbulence stability condition, similar to the principle of the energy-minimization multi-scale （EMMS） model for gas-solid systems, is formulated to close the dynamic constraint equa- tions of turbulence, allowing the inhomogeneous structural parameters of turbulence to be optimized. We name this model as the ＂EMMS-based turbulence model＂, and use it to construct the corresponding turbulent viscosity coefficient. To validate the EMMS-based turbulence model, it is used to simulate two classical benchmark problems, lid-driven cavity flow and turbulent flow with forced convection in an empty room, The numerical results show that the EMMS-hased turbulence model improves the accuracy of turbulence modeling due to it considers the principle of compromise in competition between viscosity and inertia.

Eulerian-Lagrangian simulation of distinct clustering phenomena and RTDs in riser and downer

Numerical simulation of fully developed hydrodynamics of a riser and a downer was carried out using an Eulerian-Lagrangian model, where the particles are modeled by the discrete element method （DEM） and the gas by the Navier-Stokes equations. Periodic flow domain with two side walls was adopted to simulate the fully developed dynamics in a 2D channel of 10 cm in width. All the simulations were carried out under the same superficial gas velocity and solids holdup in the domain, starting with a homogenous state for both gas and solids, and followed by the evolution of the dynamics to the heterogeneous state with distinct clustering in the riser and the downer. In the riser, particle clusters move slowly, tending to suspend along the wall or to flow downwards, which causes wide residence time distribution of the particles. In the downer, clusters still exist, but they have faster velocities than the discrete particles. Loosely collected particles in the clusters move in the same direction as the bulk flow, resulting in plug flow in the downer. The residence time distribution （RTD） of solids was computed by tracking the displacements of all particles in the flow direction. The results show a rather wide RTD for the solids in the riser hut a sharp peak RTD in the downer, much in agreement with the experimental findings in the literature. The ensemble average of transient dynamics also shows reasonable profiles of solids volume fraction and solids velocity, and their dependence on particle density.